# Graph sums in the Remodeling Conjecture

## TL;DR

This paper surveys the graph sum formulas used in proving the BKMP Remodeling Conjecture, which relates Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds to topological recursion on mirror curves.

## Contribution

It provides a comprehensive overview of the graph sum formulae and their significance in the proof of the Remodeling Conjecture.

## Key findings

- Clarifies the role of graph sums in the proof
- Summarizes the comparison between A- and B-model graph sums
- Highlights the importance of these formulas in mirror symmetry

## Abstract

The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.